Question: Simplify the following expression and state the condition under which the simplification is valid. You can assume that $q \neq 0$. $y = \dfrac{2(5q - 2)}{4q} \div \dfrac{40q - 16}{3q} $
Answer: Dividing by an expression is the same as multiplying by its inverse. $y = \dfrac{2(5q - 2)}{4q} \times \dfrac{3q}{40q - 16} $ When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 2(5q - 2) \times 3q } { 4q \times (40q - 16) } $ $ y = \dfrac {3q \times 2(5q - 2)} {4q \times 8(5q - 2)} $ $ y = \dfrac{6q(5q - 2)}{32q(5q - 2)} $ We can cancel the $5q - 2$ so long as $5q - 2 \neq 0$ Therefore $q \neq \dfrac{2}{5}$ $y = \dfrac{6q \cancel{(5q - 2})}{32q \cancel{(5q - 2)}} = \dfrac{6q}{32q} = \dfrac{3}{16} $